This invention relates to providing a Tru-Scale Octave Transformation for the Eastern Musical System (24 frequency octave), which is contrasted with the Western Musical System (12 frequency octave) with overtone collision free tones produced by both electronic instruments and fixed fretted stringed instruments of the acoustic or electronic type, and is a follow-on to, and an improvement of an invention which is disclosed in commonly assigned U.S. Pat. No. 4,860,624, and of copending, commonly assigned U.S. application Ser. No. 07/404,385, filed Sep. 8, 1989. The disclosures of that U.S. Patent and that U.S. application are incorporated herein by reference.
As stated in the New Harvard Dictionary of Music (1986), p. 778, South Asia is centered on India, and includes countries on its periphery. The treatise deals with the Great Tradition of music (as opposed to the Little Tradition which is more localized):
Among the aspects of musical theory described in the treatise (Natya Sastra, 5th century) is a tuning system of 22 intervals (Sruti) in the octave from which two heptatonic species of octave (grama) are derived. . . . After the 16th century, theoretical treatises reflect a split of the Great Tradition into two styles, now called Hindustani and Carnatic systems....The Carnatic approach emphasized a method of scale (mela) construction that would allow classification of the ragas according to their pitch content. All 72 scales possible in the 12 tone division of the octave. . .In Hindustani music, however, Bhatkhande devised a different scheme based on a group of 10 scales derived from fretting arrangements for the sitar (thata). PA1 Tru-Scale tuning involves new mathematic principles of a standard unit of measurement, related to a new measure of periodicity of wave transmission. When applied to the sound production components of an electronic instrument, primary or secondary, or other wave producing equipment, this tuning system can profoundly enhance the equipment's sound or performance. The enhancement is accomplished by eliminating the amount of dissonance caused by overtone collision by providing simultaneous frequencies with independent timespace relationships. PA1 The Tru-Scale tuning system solves the problem of dissonance by using a new mathematical base. The new base incorporates the curve imposed by nature on all moving objects, including sound waves. Current mathematics, which is used in all prior tunings, is calculated on a two dimensional plane. Tru-Scale tuning is based on a three dimensional mathematical mode. (This system takes into account the natural curve of wave travel). Therefore, intervals between waves can be calculated to move in unison with no dissonance or overtone collision. This cannot be done with current mathematical theory due to improper calculations of wave movement. Such improper calculations yield harmonic dissonance. . . PA1 The overall effect of Tru-Scale tuning creates a much cleaner and stronger sounding interval system, which in turn creates better sounding chords. The mathematical foundation behind the Tru-Scale tuning can also be used to enhance all forms of wave production, transmission and reception. PA1 The location of frets on the fingerboard provides a fixed set of tones which can be generated on any one instrument. The available tones from such an instrument is called its tonal scale. PA1 Another novel feature of this invention is a difference in the standard straight fret placement for the 12 tone, Western Music, tonal scale for a six string guitar. For equal temperament, string length is 26.2 inches (U.S. Pat. No. 4,132,143), whereas for Tru-Scale the string length is 24 inches.
The Eastern music system has posed a mathematical question for which many solutions have been offered. Some say that 22 sruti-s and 7 notes are closely related to the ratio of the circumference and radius of a circle (22/7). Some are of the opinion that this is a small number which does not introduce much error when we change ratios into additive numbers!
U.S. Pat. No. 4,860,624 teaches that:
In the present production of electronic sound, a controlled electric impulse is sent to an oscillator, in which the impulse is turned into a specific assigned frequency. It is important to note that the initial impulse, which ultimately ends up as a predetermined frequency, is determined by mathematical computations using logarithms based on the present imperfect mathematical system. These various divisions of sound, such as Equal Temperament, Just Intonation, Meantone, and Pythagorean, represent many prior attempts to divide sound into a non-dissonate interval system. The present Eastern Music system (Sruti-Scales) is said by most scholars to be based on Just Intonation.
U.S. Pat. No. 4,860,624 teaches further:
With reference to the fretted stringed musical instrument, U.S. Pat. No. 4,132,143 teaches that:
A fretted musical instrument employs one or more elements, termed frets, which function to shorten the length of a vibrating string by stopping at a precise point to thereby alter the pitch or frequency of the sound produced by the vibrating string. Fretted musical instruments may be generally divided into two categories: those having fixed frets and those having moveable frets.
Further U.S Pat. No. 4,137,813 teaches that:
As disclosed in copending, commonly assigned application Ser. No. 07/404,385:
As previously noted, the string length of the Vina (Bin), Eastern Music's main melody instrument, is at present 22 inches long, with twenty-four fixed frets. This invention provides a novel Tru-Scale string length of 24 inches, but for a 24-note scale for Eastern music, as compared to a 12-note scale for Western music, as is the subject of the copending application.